This invention relates to investigation of earth formations and, more particularly, to a method and apparatus for obtaining properties of earth formations using sonic logging and determining dipole shear anisotropy and related characteristics of the earth formations.
It is well known that mechanical disturbances can be used to establish acoustic waves in earth formations surrounding a borehole, and the properties of these waves can be measured to obtain important information about the formations through which the waves have propagated. Parameters of compressional, shear, and Stoneley waves, such as their velocity (or its reciprocal, slowness) in the formation and in the borehole, can be indicators of formation characteristics that help in evaluation of the location and/or producibility of hydrocarbon resources.
An example of a logging device that has been used to obtain and analyze sonic logging measurements of formations surrounding an earth borehole is called a Dipole Shear Sonic Imager (xe2x80x9cDSIxe2x80x9dxe2x80x94trademark of Schlumberger), and is of the general type described in Harrison et al., xe2x80x9cAcquisition and Analysis of Sonic Waveforms From a Borehole Monopole And Dipole Source For The Determination Of Compressional Arid Shear Speeds And Their Relation To Rock Mechanical Properties And Surface Seismic Dataxe2x80x9d, Society of Petroleum Engineers, SPE 20557, 1990. In conventional use of the DSI logging tool, one can present compressional slowness, xcex94tc, shear slowness, xcex94ts, and Stoneley slowness, xcex94tst, each as a function of depth, z. [Slowness is the reciprocal of velocity and corresponds to the interval transit time typically measured by sonic logging tools.]
An acoustic source in a fluid-filled borehole generates headwaves as well as relatively stronger borehole-guided modes. A standard sonic measurement system consists of placing a piezoelectric source and an hydrpohone receivers inside a fluid-filled borehole. The piezoelectric source is configured in the form of either a monopole or a dipole source. The source bandwidth typically ranges from a 0.5 to 20 kHz. A monopole source generates primarily the lowest-order axisymmetric mode, also referred to as the Stoneley mode, together with compressional and shear headwaves. It can also excite pseudo-Rayleigh mode in fast formations. A pseudeo-Rayleigh mode asymptotes to the formation shear slowness at low (cut-in) frequencies and to the Scholte waves at high frequencies. All monopole measurements provide formation properties averaged in the plane perpendicular to the borehole axis.
A dipole source excites compressional headwaves at high frequencies and dispersive flexural mode at relatively lower frequencies in both the fast and slow formations. It can also excite shear headwaves in fast formations and leaky compressional modes in slow formations. The lowest-order leaky compressional mode asymptotes to the formation compressional slowness at low frequencies and to the borehole fluid compressional slowness at high frequencies. All dipole measurements have some azimuthal resolution in the measurement of formation properties. The degree of azimuthal resolution depends on the angular spectra of the transmitter and receivers.
The radial depth of investigation in the case of headwave logging is dependent on the transmitter to receiver spacing and any in-situ radial variations in formation properties that might be present. The radial depth of investigation in the case of modal logging is well characterized and it extends to about a wavelength. This implies that the low- and high-frequencies probe deep and shallow into the formation, respectively.
Most formations exhibit some degree of anisotropy. The formation shear anisotropy can be caused by aligned fractures, thin beddings or microlayering in shales. This type of anisotropy is called formation instrinsic anisotropy. Non-hydrostatic prestresses in a formation introduce stress-induced anisotropy. A dipole dispersion crossover is an indicator of stress-induced anisotropy dominating any instrinsic anisotropy that may also be present
A present technique for measuring dipole shear anisotropy incudes recording the inline and crossline receiver waveforms from both the upper and lower dipole sources (C. Esmersoy, K. Koster, M. Williams, A. Boyd and M. Kane, Dipole Shear Anisotropy Logigng, 64th. Ann. Internat. Mtg., Soc. Expl. Geophys, Expanded Abstracts, 1139-1142, 1994). These sources are orthogonal to each other and spaces apart, for example by 6 inches. The inline and crossline receivers are oriented parallel and perpendicular to the dipole transmitter direction, respectively. A total of four sets of waveforms uxx, uxy, uyy, and uyx) are recorded at a given depth in a borehole. The first and second subscripts X and Y denote the dipole source and receiver orientations, respectively. The four sets of recorded waveforms are low-pass filtered and time-windowed and then subjected to the so-called Alford rotation algorithm that yields the fast or slow shear directions with respect to a reference dipole source direction. The recorded waveforms are then rotated by the aforementioned angle. The rotated waveforms correspond to the fast and slow flexural waveforms. These waveforms can then be processed by a known algorithm that yields the fast and slow shear slownesses, respectively. (See C. V. Kimball and T. L. Marzetta, Semblance Processing Of Borehole Acoustic Array Data, Geophysics, (49); 274-281, 1986; C. V. Kimball, Shear Slowness Measurement By Dispersive Processing Of The Borehole Flexural Mode, Geophysics, (63), 337-344, 1998.)
The described present technique for estimating formation fast shear azimuth is based on the following assumptions (see C. Esmersoy, K. Koster, M. Williams, A. Boyd and M. Kane, Dipole Shear Anisotropy Logigng, 64th. Ann. Internat. Mtg., Soc. Expl. Geophys, Expanded Abstracts, 1139-1142, 1994.)
a. It is assumed that the upper and lower dipole radiation characteristics are identically the same and that both the inline and crossline receivers are well matched.
b. The low-pass filtering of the recorded waveforms retains essentially the nondispersive part of the borehole flexural wave.
c. A depth matching of the recorded waveforms from the upper and lower dipole sources reduces the number of processed 8 waveforms to 7.
Since the Alford rotation algorithm assumes a nondispersive shear wave propagation, it is necessary to low-pass filter the recorded waveforms. Low-pass filtering of the waveforms also ensures removal of any headwave arrivals that might interfere with the shear slowness and the fast-shear direction processing of the dipole logs.
A processing time window is also selected extending over a couple of cycles at the beginning of the waveform. The placement of the processing window attempts to isolate a single flexural arrival from other possible arrivals in the waveforms.
The existing techniques have certain limitations and/or drawbacks, and it is among the objects of the present invention to provide improved technique and apparatus for determining shear slowness and directionality of anisotropic formations surrounding an earth borehole.
In accordance with a form of the invention, a system and technique are set forth that require recording of the inline and crossline receiver waveforms from only one dipole source. This eliminates the need for orthogonal source dipoles to have identical radiation characteristics. Further advantages of this approach include reduction in the amount of data and logging time to half of the referenced current procedure that requires four-component acquisition from the two orthogonal dipole sources.
As was noted above, in the existing technique, since the Alford rotation algorithm assumes a nondispersive shear wave propagation, it is necessary to low-pass filter the received waveforms. However, the more energetic part of the flexural waveforms is at somewhat higher frequencies.
As was also noted above, in the existing technique the placement of the processing window attempts to isolate a single flexural arrival from other possible arrivals in the received waveforms. However, the resulting shear anisotropy, especially the orientation of anisotropy is very sensitive to the length of the time window over which the rotation is carried out (B. Nolte, R. Rao and X. Huang, Dispersion Analysis Of Split Flexural Waves, Earth Research Laboratory Report, MIT, Cambridge, Mass., Jun. 9, 1997).
In a form of the present invention, no frequency filtering is applied to the recorded data, thereby retaining the high-energy part of the signal over the entire bandwidth.
Also, in a form of the present invention, processing is independent of the location of the dipole source and receivers in the borehole. This has the advantage that the processing can be applied to data acquired by an eccentered tool. However, the processing requires information on the location of the inline and crossline receivers in the borehole.
This processing hereof does not necessarily assume any particular rock model for the formation. It is, therefore, applicable in the presence of anisotropy caused by aligned fractures or formation stresses, and even in the presence of mechanical alteration in the borehole vicinity.
A form of the technique of the invention includes the following steps:
A. The two-component recorded waveforms (xcexcXX and xcexcXY) are processed by a matrix pencil algorithm (M. P. Ekstrom, Dispersion Estimation From Borehole Acoustic Arrays Using A Modified Matrix Pencil Algorithm, paper presented at the 29th Asilomar Conference On Signlas, Systems, and Computers, Pacific Grove, Calif., Oct. 31, 1995) separately. This algorithm separates dispersive and nondispersive arrivals in each of the two sets of 8 waveforms. In particular, this processing yields the fast and slow bandlimited flexural dispersions. As treated subsequently, the pencil algorithm is able to extract the two principal flexural dispersions from the two-component recorded waveforms (uXX and uXY) without any rotation of the recorded waveforms.
B. Small fluctuations in the fast and slow flexural dispersions due to random noise, formation heterogeneity or artifacts are eliminated from the matrix pencil algorithm by carrying out a least-squares fit to the assumed form of the flexural dispersion that extends down to lower frequencies. The low-frequency asymptote of the flexural dispersion yields the formation shear slowness of interest.
C. The fast shear direction is determined by a parametric inversion of recorded waveforms in the frequency domain. Step B ensures a well behaved quadratic objective function for inversion. The details of a new parametric inversion model is described hereinbelow.
In accordance with a form of the invention, a method is set forth for determining formation shear slowness and shear directionality of formations surrounding an earth borehole, comprising the following steps: transmitting into the formations, sonic energy from a dipole source in the borehole; measuring, at each of a plurality of receiver locations in the borehole, spaced at a respective plurality of distances from the transmitter location, signals from orthogonal wave components that have travelled through the formations; transforming the signals to the frequency domain, and separating dispersive and non-dispersive portions of the transformed signals; determining fast and slow shear slownesses of the formation from the low frequency asymptotes of the dispersive portions of the transformed signals; and determining the shear directionality of the formation by parametric inversion of the received signals. In an embodiment of the invention, the step of determining shear directionality by parametric inversion of the transformed frequency domain signals, comprises: deriving an objective function which is a function of the received signals and of model signal values at a model shear directionality; determining the particular model shear directionality that minimizes the objective function; and outputting the particular model shear directionality as the formation shear directionality. In one version of this embodiment, the objective function is a function of differences between a ratio of orthogonal model signal values and a ratio of signals from measured orthogonal wave components. In another embodiment, the objective function is a function of the distance of the measured orthogonal wave components from a subspace derived from orthogonal model signal values.